arXiv math.NTの新着論文17本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-07/

1. Series for $1/\pi$ arising from Cauchy product
2. Multiple Gauss sums
3. On $u$-Multiple Zeta Values in Positive Characteristic
4. On higher dimensional integrality and multiplicative dependence in semigroup algebraic dynamics
5. Arithmetic volume of Shtukas and Langlands duality
6. Relation between Anderson Generating Functions and Weil Pairing
7. Extensions of the Carlitz-McConnel and Blokhuis-Sziklai theorems for unions of cyclotomic classes
8. Joint extreme values of Dirichlet (L)-functions and their logarithmic derivatives
9. Settled Elements in Arboreal Galois Groups of Quadratic PCF Polynomials
10. On special values of Koshliakov zeta functions
11. A note on Bremner's conjecture and uniformity
12. Rank jumps for Jacobians of Hyperelliptic curves on K3 surfaces
13. Cohomology of special unitary groups and congruence subgroups
14. LRC codes over characteristic $2$
15. Problems and results on intersections of product sets and sumsets in semigroups
16. Cryptanalysis of the Legendre Pseudorandom Function over Extension Fields
17. Unlikely intersections in families of polynomial skew products

arXiv math.NTの新着論文19本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-06/

1. General formulas for a class of Euler sums
2. Almost Golomb Sequences
3. Higher Order Dualities over Global Function Fields and Weighted M\"{o}bius Sums over $\mathbb{F}_q{[T]}$
4. On a Conjecture about Sums Involving Farey Fractions
5. Mixed character sums modulo prime powers
6. Explicit hypergeometric modularity of certain weight two and four Hecke eigenforms
7. Equivalence between the Functional Equation and Vorono\"{\i}-type summation identities for a class of $L$-Functions
8. Large values of $L(\sigma,\chi)$ for subgroups of characters
9. Points of low degree on curves over function fields
10. A proof of Wolstenholme's theorem and congruence properties via an Egorychev-type integral
11. Functoriality and the theta correspondence
12. A generalization of Bressoud's beautiful bijection
13. p-adic Hodge theory of de Rham local systems, I: Newton polygon and monodromy
14. Algebraization of absolute perfectoidization via section rings
15. Large sum-free sets in finite vector spaces II
16. Higher order derivative moments of CUE characteristic polynomials and the Riemann zeta function
17. On de Rham--Witt Cohomology of Classifying Stacks
18. A motivic Poisson formula for split algebraic tori with an application to motivic height zeta functions
19. High-Dimensional Signal Compression: Lattice Point Bounds and Metric Entropy

arXiv math.NTの新着論文18本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-03/

1. The relativistic $p$-adic sunscreen conjecture
2. On Series Involving Cubed Catalan Numbers
3. Non-vanishing for quartic Hecke $L$-functions and ranks of elliptic curves
4. On algebraic independence of three p-adic continued fractions
5. On finite analogues of Dobi\'{n}ski's formula and of Euler's constant via Gregory polynomials
6. Overconstrained character sums over finite abelian groups and decompositions of generalized bent, plateaued and landscape functions
7. Towards the $p$-adic Hodge parameters in semistable representations of $\mathrm{GL}_n(\mathrm{Q}_p)$
8. Circle coverings driven by arithmetic sequences: a percolation approach to Diophantine approximation and fractal intersections
9. A digit-sum formula for B\"ottcher coordinates
10. The Circle Method for Quadrics over Function Fields
11. Counting Frobenius extensions over local function fields
12. On congruence conjectures of Andrews and Bachraoui
13. Worse than square-root cancellation in Bateman-Horn's conjecture
14. Large values of exponential sums with multiplicative coefficients
15. Galois group of exceptional curves on the generic del Pezzo surface
16. Cuspidal $\ell$-modular representations of ${\rm GL}_n(F)$ distinguished by a Galois involution, II
17. On the inverse Galois problem for del Pezzo surfaces of degree 1
18. Intersections and the B\'ezout Range: Abelian Varieties

arXiv math.NTの新着論文9本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-02/

1. Supersingular isogeny graphs and Hecke modules with level structure
2. The Lang-Trotter conjecture on average for genus-$2$ curves with $S_3$ reduced automorphism group
3. One-loop $p$-adic string theory and the N\'eron local height function
4. Solutions of Calabi-Yau Differential Operators as Truncated p-adic Series and Efficient Computation of Zeta Functions
5. Spectral-Dimension Obstructions for Operators with Superlinear Counting Laws
6. Hausdorff Dimension of Growth Rate Level Sets in $\theta$-expansions
7. Dynkin diagrams, generalized Nahm sums and 2d CFTs
8. Cappell-Shaneson knot pairs with the same Alexander polynomial
9. Quantum ergodicity in the Benjamini--Schramm limit for locally symmetric spaces

arXiv math.NTの新着論文20本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-04-01/

1. Truncated Plethystic Exponentials Preserve Power Sum Constraints
2. On Eisenstein series identities and new identities connecting Ramanujan-G\"ollnitz-Gordon continued fraction and Ramanujan's continued fraction of order four
3. On non-Archimedean and motivic distributions defined by kernels
4. Congruences and ramified primes in fields of coefficients of newforms
5. $D(-1)$-triples of triangular numbers
6. Analytic rank-one elliptic curves over function fields and their rank over certain ring class fields
7. From Orientations to $\ell$-adic Period Vectors
8. Weber modular curves and modular isogenies
9. $p$-adic Character Neural Network
10. ABC implies that Ramanujan's tau function misses almost all primes
11. Various conjectural series identities
12. A counterexample to a conjecture of S\'ark\"ozy on sums and products modulo a prime
13. Some geometric series for Euler's constant
14. Composition of random functions and word reconstruction
15. Hypergeometric Bernoulli Polynomials Defined on Simplicial $d$-Polytopic Numbers
16. Uniform optimal-order Wasserstein quantisation
17. A Finite-State Proof of the Well-Definedness of a Perturbed Hofstadter Sequence
18. Reciprocity of Skew Hall-Littlewood-Schubert Series
19. Non-Archimedean Analogue of Chase's Lemma
20. Short proofs in combinatorics and number theory

arXiv math.NTの新着論文32本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-03-31/

1. A categorical p-adic Langlands correspondence for GL_2(Q_p)
2. Tempered vs generic automorphic functions and the canonical filtration on automorphic functions
3. Asymptotic Universal Koszulity in Galois Cohomology
4. Improved Bounds for 3-Progressions
5. A note on the multiple zeta functions and their variants at identical arguments
6. NP-hardness of SVP in Euclidean Space
7. The congruence subgroup property for $S$-arithmetic subgroups of simple algebraic groups when $S$ has positive Dirichlet density
8. Monodromy groups of polynomials of composition length 2
9. Sharp Hausdorff Dimension Bounds for Sets with Bounded and Growing Digits in $N$-expansions
10. Galois representation of the product of two Drinfeld modules of generic characteristic
11. The Davenport-Lewis-Schinzel problem on the reducibility of $f(X)-g(Y)$
12. Some vanishing results for the rational completed cohomology of Shimura varieties
13. On the locally analytic completed cohomology of modular curves
14. Products of consecutive integers with unusual anatomy
15. Zeta Zeros in a Narrow Vertical Box
16. Plectic Heegner classes
17. Special geodesics and atypical intersections
18. Farey graphs and geodesic expansions of complex continued fractions
19. Complete Walsh spectra for a permutation-inverse family of Boolean functions
20. The conjecture of Colmez and reciprocity laws for modular forms
21. One continuum class of fractal functions defined in terms of $Q^*_s$-representation
22. Numeral systems with non-zero redundancy and their applications in the theory of locally complex functions
23. On the satisfaction frequency of spectral characterization conditions
24. Structure of the Components of the Fixed Locus of a Self-Map of the Berkovich Line
25. A short proof of Erd\H{o}s's $B+C$ conjecture
26. English translation of Frobenius' and Stickelberger's "On the theory of elliptic functions"
27. Root lattices over totally real fields
28. Motivic counting of curves on split quintic del Pezzo surfaces
29. On Generalizations of Maiorana-McFarland and $\mathcal{PS}_{ap}$ Functions
30. Zeros in the character table of the symmetric group
31. Optimal bounds for an Erd\H{o}s problem on matching integers to distinct multiples
32. Weakly special varieties, Campana stacks, and Remarks on Orbifold Mordell

arXiv math.NTの新着論文14本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-03-30/

1. On bilinear sums with modular square roots and applications III
2. On nonconvex constellations among primes I
3. Examples of Quadratic Polynomials over $\mathbb{Q}$ with Surjective Arboreal Galois Representations
4. Surviving Eratosthenes sieve I: quadratic density and Legendre's conjecture
5. On a M\"obius double sum
6. Uniform Diophantine approximation with restrictions via total density of collections of subspaces
7. Exactness property of Breuil-Kisin functors and Bloch-Kato Selmer groups
8. Finiteness of Disjoint Covering Systems with Precisely One Repeated Modulus
9. A further $q$-generalization of the (C.2) and (G.2) supercongruences of Van Hamme
10. Proof of Hong's conjecture on divisibility among power GCD and power LCM matrices on gcd-closed sets
11. Arithmetic sums and products of infinite multiple zeta-star values
12. Van der Waerden's theorem on arithmetic progressions -- a survey of some historical and modern developments
13. Resonances on geometrically finite graphs
14. Integral Means Spectrum for the Random Riemann Zeta Function

arXiv math.NTの新着論文21本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-03-27/

1. On $\frac{1}{n!}$ in Cantor sets
2. 2- and 3-Dissections of Second-, Sixth-, and Eighth-Order Mock Theta Functions
3. On the Density of Coprime Reductions of Elliptic Curves
4. Igusa Stacks and the Cohomology of Shimura Varieties II
5. Arithmetic exceptionality of Latt\`{e}s maps
6. Weak approximations, Diophantine exponents and two-dimensional lattices
7. Analytical continuation of prime zeta function for $\Re(s)>\frac{1}{2}$ assuming (RH)
8. Stern polynomials and algebraic independence
9. The Prime times of twisted Diophantine approximation
10. Second order Recurrences, quadratic number fields and cyclic codes
11. Computing the local $2$-component of a non-selfdual automorphic representation of $\mathrm{GL}_3$
12. Poly-Bernoulli numbers from shifted log-sine integrals
13. A note on gamma factors for pairs
14. An integrality phenomenon
15. Murmurations in the depth aspect
16. A conditional bound for the least prime in an arithmetic progression
17. Iterated beta integrals
18. Quadratic Residue Codes over $\mathbb{Z}_{121}$
19. Linear theories of global fields with absolute values
20. Local coherence for representations of amalgams
21. Exceptional loci in algebraic surfaces

arXiv math.NTの新着論文13本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-03-26/

1. Period integrals of distinguished polarised strongly tempered hyperspherical varieties
2. Notes on Cyclotomic Function Fields with Quadratic Modulus
3. On Selmer complexes, Stark systems and derived $p$-adic heights
4. The average number of representations of an integer as a sum of two prime powers over multiples of a fixed integer
5. Kobayashi length bounds on bordered surfaces and generalized integral points on abelian varieties
6. Class number zeta function of imaginary quadratic fields
7. On the Quartic Invariant of Odd Degree Binary Forms
8. Additive Rigidity for Images of Rational Points on Abelian Varieties
9. Legendre compressions and an integrality conjecture for the H\"ormander--Bernhardsson extremal function
10. On Maximal Values of Gronwall Numbers for Integers with Given Greatest Prime Factor and Remainder in Modified Mertens Formula
11. On the paucity of lattice triangles
12. Weighted Cohomology, Hodge Theory and Intersection Cohomology of Shimura varieties
13. A central limit theorem for connected components of random coverings of manifolds with nilpotent fundamental groups

arXiv math.NTの新着論文21本をご紹介します。

番組ページ: https://prepridondon.nyoho.jp/channels/math-nt/episodes/2026-03-25/

1. Anticyclotomic Iwasawa main conjectures for modular forms
2. Density of Visible Lattice Points on Hyperplanes and their Intersections
3. Admissible pairs and $p$-adic Hodge structures III: Variation and unlikely intersection
4. On the series expansion of k-free Dirichlet series and its analytical continuation
5. Murmurations, Periods, and Local Factors
6. On generalized Thabit numbers $(p+1)p^\mathfrak{a}-1$ in the $k$-Lucas sequence
7. $p$-adic multiple zeta values of integer indices
8. The second minimum of Barnes-Wall lattices
9. Symmetric measures of pseudorandomness for binary sequences
10. Short Exponential Sums and Ternary Correlations of Multiplicative Functions
11. Branches of Markoff $m$-triples with two $k$-Fibonacci components
12. Counting points in thin sets: A survey
13. Bohr's Last Problem Under the Entirety Hypothesis: A Survey with Initial Reductions
14. Uniform boundedness of small points on abelian varieties over function fields
15. Mahler series with multiplicative coefficient sequences
16. Partition regularity in imaginary quadratic rings of integers
17. Picard rank jumps for families of K3 surfaces in positive characteristic
18. Construction of graph coverings with prescribed Iwasawa invariants
19. Cohomological descent for obstructions to local-global principle
20. Eulerian polynomials and the alternating sum of excedances
21. Exponential motives on the affine Grassmannian